With a bid unit to Egypt, you had better just leave Egypt alone and hit the following:
sz2 use 1 ss, 1 fig, 1 bmb
sz6 use 1 ss, 1 fig (+ 1 ca if you feel like it)
sz12 use 1 ss, 2 fig
take Gibraltar with an infantry from France or Algeria to help Italy get its NO
on Italy 1, you can hit Egypt or Trj, whichever, or both if the UK pulled back to Sudan. Just make sure to get both of your NO’s so as to get the money flowing. If the UK pulled out of Egypt so that your Libyian troops can take it, you could even move the fleet to sz13, dropping off 1 inf, 1 arm in Algeria so that on Italy 2 you could take Brazil with the infantry unit if the US is headed to the Pacific, but the armor unit could still go to Egypt on Italy 2.
This should accomplish what you need to accomplish.
Also, you should buy at least 1 air unit on G1 (preferably a bomber), so as to keep the pressure up on the UK Atlantic fleet since you should have decimated it.